The walls weren’t even up yet on the granny flat Limei Huang is building in her San Jose backyard when people started lining up to rent the space.

The first offer came from the worker who laid the unit’s foundation. After his day’s work, he called Huang up and asked: When it’s finished, can I move in? Not long after, Huang brought in a painter. While he was giving her an estimate, he asked the same question. She had to tell him to get in line.

“I haven’t put it on the market,” said Huang, “and already people are looking for it.”

Huang is part of a growing group of Bay Area homeowners taking advantage of changing laws and an intense demand for housing by building small dwellings known as granny flats or in-law units in their backyards, converted basements or garages.

Cities around the Bay Area report a dramatic uptick in the number of people applying to build the units, with applications over the past year increasing by more than 1,000 percent in some places. Experts predict interest will grow even more this year as legislators and local cities continue to propose new, granny flat-friendly policies, possibly bringing some relief to the housing shortage that has driven the price of renting or buying a home through the roof.

“This is going to be a major piece of the solution to our housing crisis in the next decade,” said Matt Regan, senior vice president of public policy for the Bay Area Council.

The number of building permit applications San Jose received for in-law units, officially called accessory dwelling units, increased five-fold between 2015 and last year — jumping from 28 to 166 — according to a recent report from UC Berkeley’s Terner Center for Housing Innovation. In Oakland, the number of applications submitted during that time grew from 33 to 247. And in San Francisco they spiked from 41 to 593 — an increase of nearly 1,340 percent.

Adding a few hundred in-law units here and there won’t fix the region’s chronic housing shortage. But as support grows from state lawmakers, city leaders and the private sector, experts expect the Bay Area soon will have a sizable supply of these small houses. After Senate Bill 1069 became law last January, slashing the price for building an in-law unit by as much as $60,000 for some homeowners, the legislature this session will consider another bill that goes even further to remove hurdles from building the units. Meanwhile, cities from Oakland to San Jose have loosened their own restrictions.

All those changes have led to a booming business for Steve Vallejos of Valley Home Development, a Fairfield-based developer who specializes in in-law units. A year ago, his company was fielding one or two granny flat requests per month. One week into January, Vallejos already had five requests and expects the company probably will end the month with 11 or 12.

“The growth has been pretty dramatic,” Vallejos said.

Building a granny flat allowed 31-year-old Megan Kellogg to move back to the Richmond neighborhood where she grew up, a move she couldn’t otherwise afford. Kellogg, an opera singer, is finishing construction on a 300-square-foot unit in the backyard of her childhood home. When it’s complete, Kellogg’s mother will move into the unit, and Kellogg, her husband and their 3-year-old son will take her place in the main house.

“The opportunity was just too good to turn down,” said Kellogg, who had been living in Washington, D.C. before returning to Richmond. She spent about $88,000 on the project, and now plans to split the mortgage on the main house with her mother. It will be less than her family spent to rent a home on the East Coast.

Sen. Bob Wieckowski, D-Fremont, wants to help more people like Kellogg. A year ago, his first bill eased parking, zoning and lot-size requirements that, he said, were so cumbersome that few homeowners built in-law units — at least, legally.

His new bill, introduced last week, would force cities to eliminate most of the fees they charge for construction of new in-law units, a shift Fremont made late last year. Such fees, charged for everything from utilities connections to schools, vary widely but can total tens of thousands of dollars and are often blamed for increasing the cost of housing. Many in-law units, the senator said, have been driven underground as a result. Senate Bill 831 also would create a temporary amnesty program for unpermitted in-law units.

“Let’s bring these people out of the darkness,” Wieckowski said, “and let them have a documented home that they’re paying taxes on.”

Wieckowski’s new legislation is certain to draw opposition from cities and others who see the proposal as a further erosion of local control over land use and planning amid the housing crisis. The measure further eases parking restrictions and requires cities to automatically approve an in-law unit application that has collected dust in a city office for 120 days.

In-law units can be an important tool for cities to address their housing shortages, said Jason Rhine, a lobbyist for the League of California Cities, which opposed Wieckowski’s 2016 pro-in-law unit bill. “Where we become concerned,” he said, “is when the state is trying to micromanage where and how.”

If the state prevents local governments from collecting fees, Rhine asked, how will a city pay for the services those new residents need?

The League urged Gov. Jerry Brown to veto Wieckowski’s first in-law unit bill, arguing that easing restrictions could lead to “impaired neighborhood character,” increase competition for parking spots, and threaten the privacy of existing homeowners.

For Huang, building an in-law unit to generate additional rental income seemed like a no-brainer. She hopes to put the 600-square-foot unit on the market in March, potentially charging about $2,000 a month. Now she’s adding the finishing touches. When it’s done, she estimates she will have spent about $100,000 and five months on the project, adding: “It’s been a lot easier than I would expect.”